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Vaselesa [24]
3 years ago
10

What is the solution of the following trig equation: tan(theta)(csc(theta)+2)=0

Mathematics
1 answer:
gtnhenbr [62]3 years ago
7 0
D:\theta\neq\frac{k\pi}{2};\ k\in\mathbb{Z}\\\\tan\theta(csc\theta+2)=0\iff tan\theta=0\ \vee\ csc\theta+2=0\\\\\\tan\theta=0\iff\theta=k\pi\notin D\\\\csc\theta+2=0\\\\csc\theta=-2\\\\\frac{1}{sin\theta}=-2\\\\-2sin\theta=1\ /:(-2)\\\\sin\theta=-\frac{1}{2}

(\theta=-\frac{\pi}{6}+2k\pi\ \vee\ \theta=\frac{7\pi}{6}+2k\pi)-answer
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